CUTh-Solver: GPU-Accelerated Sparse Matrix Solver for High-Resolution Thermal Simulation of 3D ICs

2026-06-16

AI Summary

This work addresses the challenge of efficiently solving structured, sparse, symmetric positive-definite systems arising in high-resolution thermal simulation of 3D integrated circuits, where general-purpose GPU sparse solvers struggle to achieve high performance. To this end, the authors propose CUTh-Solver, a GPU-accelerated preconditioned conjugate gradient (PCG) framework tailored for this domain. Its key innovations include a compressed diagonal storage format (cDIA), diagonal-level sparse matrix-vector multiplication (SpMV) to coalesce memory accesses, a highly parallelizable preconditioning strategy, and an adaptive fine-grained mixed-precision mechanism that enhances throughput while preserving numerical stability. Experimental results demonstrate that CUTh-Solver achieves up to 25.8× speedup over GPU-accelerated COMSOL Multiphysics 6.4 and more than 3× acceleration compared to general-purpose libraries such as NVIDIA AmgX, cuSPARSE, and cuDSS, with ablation studies confirming the effectiveness of each optimization component.

Abstract

Coarse-grained thermal simulation tends to underestimate localized thermal issues, potentially missing critical hotspots. Accurate analysis, therefore, demands fine-grained information, which dramatically increases grid resolution and thus computational workload. Fortunately, the coefficient matrices are often sparse with regular sparsity patterns, offering optimization opportunities. However, existing general-purpose matrix solvers on GPUs rarely exploit these domain-specific properties, thereby encountering bottlenecks in data storage, memory access, parallelism, computational efficiency, and hardware utilization. Therefore, we propose CUTh-Solver, a co-designed GPU-accelerated Preconditioned Conjugate Gradient (PCG)-based sparse solver framework for Symmetric Positive Definite (SPD) systems arising from high-resolution steady-state and transient 3D IC thermal simulation. For data storage, CUTh-Solver condenses the Diagonal (DIA) storage format to remove redundancy. To optimize the memory access, CUTh-Solver employs diagonal-wise SpMV to achieve coalesced memory access. We further observe a critical conflict between parallelism and preconditioning quality and thus adopt a high-parallelism preconditioning strategy. To improve computational efficiency and hardware utilization, we employ an adaptive fine-grained mixed-precision strategy that leverages diverse floating-point units to avoid resource contention, enhancing throughput without compromising numerical stability. Experimental results show that CUTh-Solver achieves up to 25.8x speedup over GPU-accelerated COMSOL Multiphysics 6.4 and over 3x speedup over NVIDIA's native general-purpose libraries (AmgX, cuSPARSE, cuDSS). Ablation studies validate the individual contribution of each optimization. The code is available at: https://github.com/Chenghan-Wang/CUTh-Solver

Problem

• 3D IC thermal simulation
• sparse matrix solver
• GPU acceleration
• high-resolution simulation
• SPD systems

Innovation

• GPU acceleration
• sparse matrix solver
• mixed-precision computing
• thermal simulation
• 3D ICs